Red Clearance Intervals: Theory and Practice

At signalized intersections the red clearance interval has to be long enough to prevent accidents, but no longer than necessary in order to ensure efficient traffic operations and encourage respect of the yellow and red indication. Because designers were using a variety of methods to calculate clearance times, a Dutch association of traffic control engineers called CVN initiated the development of a generally applicable method. The resulting method is based on a driver behavior model that involves five parameters. In contrast with the suggested ITE method, it determines red clearance time for each ordered pair of conflicting streams, depending on the distance of the entering and exiting streams from zone within the intersection where the two streams’ paths first overlap. The conflict zone method was calibrated using field data collected at two intersections, and has been included in the 1996 Dutch guidelines for traffic controllers. In comparison with the ITE suggested method, which gives the exiting stream enough time to clear the entire intersection, the new method is sensitive to the sequence in which traffic streams appear in the cycle, and tends to call for less clearance time, improving intersection capacity and reducing delay. This approach is especially beneficial in improving the efficiency of intersections with actuated control. Muller, Dijker & Furth 3 The vehicle signal change interval is “that period of time in a traffic signal cycle between conflicting green intervals” (1, p. 295). This interval may consist of a yellow change interval only or both a yellow change interval and a red clearance interval (also called an all-red interval). While in the U.S. use of a red clearance interval is a matter of local policy, in the Netherlands the red clearance interval is always required. However, the applied lengths of red clearance intervals vary strongly in practice because of lack of a generally accepted calculation method. For the U.S., a similar situation is recognized by (2, p. 33), stating that “there is currently no nationally recognized recommended practice for determining the change interval length, although numerous publications provide guidance.” To standardize the calculation of red clearance intervals, an informal association of Dutch traffic control engineers, the Contactgroep Verkeersregeltechnici Nederland (CVN), identified in 1992 the need to for a rational method grounded in both theory and observation of motorist behavior. In response, the Transportation Research Laboratory of the Delft University of Technology was funded by the national Ministry of Transport and the cities of Amsterdam and Rotterdam to carry out the needed research to develop a the new method, which was subsequently accepted and published as a guideline by the Dutch Ministry of Transport (3). The new method leaves unchanged guidelines regarding the yellow interval. Longstanding Dutch practice is to time the yellow interval in order to avoid a dilemma zone, just as described in the 1994 “ITE method” (4). The yellow time formula is dec appr r yellow a v t t 2 + = (1) where tr = reaction time, vappr = approach speed (85-percentile approach speed is typically used), and adec = deceleration rate. However, this formula for yellow time demands a complementary formula for red clearance time, because the yellow time formula is based on cars entering the intersection throughout the yellow interval. The formula developed follows the general Dutch practice of determining needed red clearance time for each paired sequence of conflicting traffic streams, comparing the travel time for both traffic streams to the point where their paths conflict. The innovation of the new method is how it deals with the danger posed by drivers who see the signal turn green before they come to a stop and therefore enter the intersection at greater speed than drivers who came to a standstill before the signal turned green. First, the driver behavior model is presented, and from it the derivation of an equation for necessary red clearance time. Next, data collected at two intersections is analyzed to estimate parameters of the model and to verify that it matches observed driver behavior. Finally, we offer a brief comparison of the new method with current U.S. practice, and then draw conclusions. A NEW METHOD TO DETERMINE RED CLEARANCE TIMES With the yellow interval timing formula (eq. 1) used by Dutch traffic control engineers and suggested by ITE, vehicles must be expected to enter the intersection (cross the stop line) during the entire yellow interval. The purpose of the red clearance interval -the interval between the start of red for one traffic stream and the start of green for the succeeding conflicting traffic stream -is to ensure that traffic in the second stream can safely enter the intersection without colliding with the last vehicle legally entering from first stream. While clearance intervals are important for safety, they also impact traffic operations: they contribute to lost time and, as such, affect delays, queuing, and necessary cycle length. In principle, then, clearance times should be as small as possible while still allowing a traffic stream to safely follow a conflicting stream. ITE’s suggested red clearance time (“all red time”) is based on the principle that traffic in the entering stream should wait until the a vehicle from the previous stream that enters the intersection in the last moment of yellow completely clears the intersection; that is, Muller, Dijker & Furth 4 speed on intersecti the clear to distance tclearance = (2) The new approach, which may be called the conflict zone approach, is more precisely targeted. The Dutch practice of stream-based vehicle actuated traffic signal control requires that before a traffic stream can get a green indication, it must satisfy clearance times for every conflicting traffic stream that just turned red. As an example, several traffic streams at a typical intersection are shown in Figure 1. Red clearance times must be supplied to the controller for each ordered pair of conflicting streams (i, j), where i = index of the stream getting the red (the “exiting stream”) and j = index of the stream whose green immediately follows (the “entering stream”). If, in the Figure 1 example, traffic streams SBT and NBT are followed by conflicting streams EBL and EBT, and if the exiting streams begin red simultaneously, stream EBL could not begin green until clearance times tclearance(SBT, EBL) and tclearance(NBT, EBL) had both expired, and stream EBT could not begin green until clearance times tclearance(SBT, EBT) and tclearance(NBT, EBT) had both expired, where tclearance(i,j) = specified clearance time between the start of stream i’s red start and stream j’s green start. In practice, differences in clearance times between stream pairs often mean that one entering traffic stream gets the green slightly before another. For a given ordered pair of conflicting movements, clearance time is based on the travel time of vehicles in the exiting and entering stream to that stream pair’s “conflict zone,” the area within the intersection where paths taken by vehicles in the two streams first overlap. Let sesit equal the distance from the stop line a vehicle in the exiting stream must travel to fully clear the conflict zone (including the vehicle length, commonly taken to be 12 m so as to represent a truck), and let tesit equal an exiting vehicle’s travel time from the stop line to just beyond the conflict zone; similarly, let sentrance equal the distance from the stop line of the entering stream to the conflict zone, and let tentrance equal the amount of time the first vehicle from the entering movement needs to reach the conflict zone. To avoid a collision, the length of the red clearance interval, tclearance(i,j) must be ( ) ( ) ( ) j t i t j i t entrance exit clearance − = , (3) In the interest of safety, the exit time should concern a relatively slow vehicle, while the entrance time should pertain to a fast vehicle. The sketch in Figure 1 illustrates the importance of determining clearance time as a function of an ordered pair of streams. Consider the conflict zone between conflicting streams SBT and EBT. As one can see, EBT’s stop line is much closer to the conflict zone than is SBT’s. Consequently, if EBT is exiting while SBT is entering, little or no red clearance will be needed, because EBT vehicles have a considerable amount of time to clear the conflict zone before a SBT vehicle arrives. On the other hand, if SBT runs first followed by EBT, a considerable red clearance time will be needed, because an EBT vehicle could arrive very quickly at the conflict zone, well before the last SBT vehicle had cleared if it entered the intersection just at the end of yellow, unless stream EBT traffic is delayed by a red clearance interval. In the remainder of this paper, the stream indices i and j will be suppressed. Determination of Exit Time The new method does not change the calculation of exit time, which is calculated rather straightforwardly as exit exit exit v s t / = (4) where vexit equals the speed of a vehicle in the exit stream that crosses the stop line at the last moment of yellow. Because such a vehicle was presumably unable to stop during the yellow interval, its speed is unlikely to be below the average approach speed; nevertheless, a somewhat conservative value may still be used. However, no such generally accepted method existed for entrance time. The next section describes the method that was developed to fill this gap. Muller, Dijker & Furth 5 Determination of Entrance Time In comparison to the calculation of exit times, the calculation of entrance times is more complex. For vehicles that decelerate to a standstill at the stop line before the light turns green, entrance time can be determined easily enough based on an assumed acceleration trajectory. However, consider a vehicle approaching the stop line that has started to decelerate because the signal is red, but before it comes to a standstill, the signal turns green. That vehicle can then begin to accelerate and enter the intersection at some speed. Such a vehicle may well reach the conflict zone sooner than it would have if it had been standing at the stop line when the signal turned green. Depending on the position and speed of the entering vehicle when the traffic signal turns green, the entrance time could differ. For safety, clearance time should be based on the smallest possible entrance time. To determine clearance time according to the complex situation described above, a model of driver behavior is required. The following model is used: • a driver with no traffic ahead of it approaches the intersection with an approach speed vappr • seeing a red signal, drivers decelerate as late as possible with constant deceleration adec following a trajectory that, if uninterrupted, brings them to a standstill at the stop line • when the signal turns green, drivers accelerate with the constant acceleration aacc until they reach the speed vmax • a reaction time between when the light turns green and acceleration begins may be taken into account. To obtain safe values for the clearance time, the parameters for the described model should represent a rather aggressive driver. Graphical Derivation of Minimum Entrance Time Consider a vehicle facing a red signal as it approaches an intersection with speed vappr = 50 km/h, decelerating to a standstill at the stop line with adec = -3 m/s 2 and then immediately accelerating at aacc = 2 m/s . If reaction time is assumed to be zero, that would imply that the vehicle came to a stop at the moment the signal turns green; if reaction time tr is non-zero, that would imply that the signal turned green an interval tr before the vehicle came to a standstill. The vehicle’s deceleration to a standstill is completed during that reaction time, and so acceleration an interval tr after the signal turns green. The vehicle’s trajectory is plotted as the heavy line in Figure 2(a). The coordinate system used for this figure shows distance s on the horizontal axis, with s = 0 at the stop line, and time τ on the vertical axis. The origin of time, that is, τ = 0, is placed at the “moment of effective green,” which is the moment of first possible acceleration, an interval tr after the signal turns green. Note that s and τ can be expressed as functions of each other. For a given distance to the conflict zone s = sentrance, tentrance(s) = τ( s) + tr. Because of the coordinate system used, it is convenient to define adjusted entrance time as entrance time minus reaction time, that is, t'entrance = tentrance tr (5) so that t'entrance(s) = τ( s). Next, consider what would happen if the light turned green early enough during the vehicle’s deceleration that the driver had time to react and then begin accelerating before reaching the stop line. Define tx as time interval between the moment at which the vehicle’s deceleration trajectory would have led to a standstill if uninterrupted and the moment of effective green (when the vehicle begins to accelerate). For a vehicle that comes to a complete stop, tx is positive, and for a vehicle that never comes to a complete stop, tx is negative. The dashed line in Figure 2(a) represents the trajectory of a vehicle with tx = -1.5 s. Comparing with the solid line, for which tx = 0, one can see that both vehicles start decelerating at the same distance from the stop line. Until the moment of effective green, the dashed curve, compared to the solid curve, is simply shifted vertically by tx, the difference between the start of effective green for the two cases. For the second vehicle as well as the first, adjusted entrance time for a given entrance distance s can simply be read from the figure as t'entrance(s) = τ( s). Muller, Dijker & Furth 6 One can see in Figure 2(a) that for very small distances from the stop line, entrance time is smaller for the vehicle that comes to a standstill, while for greater entrance distances, entrance time is smaller for the vehicle that passes the stop line with some speed. In Figure 2(b), trajectories are drawn on the same coordinate system for a range of values of tx between 0 to -5 s, showing only the part of the trajectories occurring after the stop line. The upper envelope of these trajectories represents the minimum adjusted entrance time for any entrance distance. In the following subsection, the curve representing this envelope will be derived analytically. Analytical Derivation of Minimum Entrance Time Again, consider a vehicle approaching an intersection, facing a red signal, with no traffic ahead of it, and following the behavior model described previously. The coordinate system will now be adjusted by placing the origin of time τ at the moment at which the approaching vehicle’s trajectory would come to a stop at the stop line if that vehicle’s deceleration is not interrupted by the signal becoming green. Let τg = start of effective green (i.e., start of green plus reaction time). Then, under the new coordinate system,